We will use the above expression to calculate the ADM mass in an AdS\(_3\)  background. Note that if \(A(R)=A_0(R)\)  one obtains \(M=0\)  which implies that our definition has set empty AdS\(_3\)  space to have zero mass. This is the desired and expected result since maximally symmetric spacetimes can be viewed as the ground states of General Relativity [1]} and as such are typically set to zero energy.
